The term "eye-pit" refers to a hollow or depression that surrounds the eye. It's a lesser-known term that can be difficult to find synonyms for. However, there are a few options to consider. "Orbital socket" is a more medical term that refers to the bony structure that surrounds the eye. "Eye socket" is a simpler, more commonly used variation of this term. "Ocular recess" is another synonym that describes the depression surrounding the eye. These terms may come in handy for medical professionals or those who enjoy delving into anatomy, as they all refer to the same structure in the human body.